Chebyshev's bias against splitting and principal primes in global fields

This work addresses the prime number races for non-constant elliptic curves E E over function fields. We prove that if r a n k ( E ) > 0 \mathrm {rank}(E) > 0 , then there exist Chebyshev biases towards being negative, and otherwise there exist Chebyshev biases towards being positive. The key input is the convergence of the partial Euler product at the centre, which follows from the Deep Riemann Hypothesis over function fields.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Chebyshev's bias against splitting and principal primes in global fields

Cited by 3 publications

References 27 publications

Chebyshev’s bias for Fermat curves of prime degree

Chebyshev’s bias for Fermat curves of prime degree

Chebyshev's bias against splitting and principal primes in global fields

A new aspect of Chebyshev’s bias for elliptic curves over function fields

Contact Info

Product

Resources

About